Let's consider how rotations work in PBSTs. Here's the usual
illustration of a rotation:

As we move from the left side to the right side, rotating right at
Y, the parents of up to three nodes change. In any case, Y's
former parent becomes X's new parent and X becomes Y's new
parent. In addition, if b is not an empty subtree, then the parent
of subtree b's root node becomes Y. Moving from right to left,
the situation is reversed.